Answer:
Hector's kite is 61.84 feet from the ground.
Step-by-step explanation:
The angle of elevation of the kite is 42°15’30” when converted to decimals, it is ≅
Let the height of the kite to the horizontal of angle of elevation be represented as x. Applying the trigonometric function to the sketch of Hector's kite,
Sin θ =
Sin =
⇒ x = 86 x Sin
= 86 x 0.6725
= 57.835
x ≅ 57.84 feet
The height of Hector's kite from the ground = x + 4
= 57.84 + 4
= 61.84 feet
Answer:
The value of the expression at x=5 is 10
Step-by-step explanation:
The given expression is
Let us simplify this expression.
Distribute -2 over the parentheses, we get
Now, substitute x = 5, we get
On simplifying, we get
The value of the expression at x=5 is 10
Answer:
We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.
Step-by-step explanation:
We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.
You select a sample of 100 light bulbs and find mean bulb life is 490 hours.
Let = <u><em>population mean light bulb life.</em></u>
So, Null Hypothesis, :
500 hours {means that the population mean light bulb life is at least 500 hours}
Alternate Hypothesis, :
< 500 hours {means that the population mean light bulb life is below 500 hours}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean bulb life = 490 hours
σ = population standard deviation = 50 hours
n = sample of light bulbs = 100
So, <u><em>the test statistics</em></u> =
= -2
The value of z test statistics is -2.
<u>Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.</u>
Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis.</u>
Therefore, we conclude that the population mean light bulb life is at least 500 hours.